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MathGroup Archive 2001

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Re: Assumptions question (1/m^x,x>1,m=Infinity)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg31112] Re: Assumptions question (1/m^x,x>1,m=Infinity)
  • From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
  • Date: Wed, 10 Oct 2001 19:14:31 -0400 (EDT)
  • References: <9pjgnp$3ge$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

gg at hugo.doemaarwat.nl (Hugo Buddelmeijer) wrote:
> How do I simplify this:
> 1/m^x
> when I know that x>1 and m is extremely large, so this term cancels
> and becomes 0.
> I'm thinking about something like:
> Simplify[Limit[1/m^x,m->Infinity],x>1]
> But I can't get math to figure out what I meant, I've tried about all
> possible things with Simplify, Limit and Assumptions that I've realy
> run out of ideas..

Here is an "almost solution", but I doubt it will be useful to you.
Use something like

 Limit[1/m^Interval[{1,1000}],m->Infinity]

which does yield 0. One trouble with this method -- using interval
arithmetic -- is that a specific finite upper limit for x must be
given. This should not be the case; specifically, we should be able
to use

 Limit[1/m^Interval[{1,Infinity}],m->Infinity]

but this does not simplify to 0 as it should, perhaps because
Mathematica thinks, incorrectly, that Infinity^Interval[{1,Infinity}]
is Indeterminate.

BTW, do people from Wolfram Research read this newsgroup and take
appropriate note of errors reported here, or should we always submit
errors to Wolfram Research directly?

  David

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